Abstract.
Empirical properties of generating systems for complex reflection groups and their braid groups have been observed by Orlik-Solomon and Broué-Malle-Rouquier, using Shephard-Todd classification. We give a general existence result for presentations of braid groups, which partially explains and generalizes the known empirical properties. Our approach is invariant-theoretic and does not use the classification. The two ingredients are Springer theory of regular elements and a Zariski-like theorem.
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Oblatum 7-XII-2000 & 22-III-2001¶Published online: 20 July 2001
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Bessis, D. Zariski theorems and diagrams for braid groups. Invent. math. 145, 487–507 (2001). https://doi.org/10.1007/s002220100155
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DOI: https://doi.org/10.1007/s002220100155